I do respect the way Anne has managed (admittedly its taken years) to create her "working" role and still remain rather private and have her own family life that isn't all based around them being working official royals. Its as close to perfect as royal life can get IMO - a very distinct public role that is very business like vs a clearly very close and loving private family life.
I think one of the reasons why Anne managed to be private besides the fact that she is a minor royal is because she wasn't glamorous enough for the mainstream media. While she was considered beautiful and glamorous in her youth, the media might thought of her personality as "unladylike", it also didn't help that Diana and Fergie who were young and beautiful came into the royal scenes. Heck, Lady Kitty Spencer isn't a royal but there are more articles about her than Anne, so it's pretty clear that looks play a major factor here. However, knowing Anne, she probably isn't bothered by what the media are writing about her.